Here's how to temp fix white covers. Wait till it's late at night. I do mine around 3AM then turn WiFi on and tap on the gear then applications\All apps\ Kindle App\ Clear Data then hit Home.
Do not do anything while it's syncing. Once it's done go to the doc tab and the covers should be fixed now. It may take doing this twice to fix them all.

Thanks for the tip. I tried it just now (1am Pacific time) and it mostly worked. The first two times I tried it didn't help. The third time, instead of hitting home after clearing the data I shut the Fire down. When I restarted, it showed covers for all books everywhere, except for one on the carousel. What's weird is that was one of the books that was working before. Now it doesn't even have the generic cover with text; it just shows a gray rectangle. If I add it to my favorites the cover shows fine there, but still not on the carousel. Your trick for fixing that doesn't seem to help. I wouldn't be surprised if it fixed itself in the near future.

Sigh, what a buggy release. A lot of people seem to be having trouble with covers and regardless of what support told mkgtu, there's no way one-way syncing is intentional.